Solution: For Simple Interest: A = (P × R × T)/100 P = ₹ 12,000 T = 2 years R = 6% simple interest where , A = Amount, P = Principal, T = Time period in years and R = Rate percent\ Simple Interest to be paid for 2 years at the rate of 6% per annum S.I. for 2 years = 2 × 12000 × (6/100) = 2 × 120 × 6 = 1440 For Compound Interest: A = P[1 + (r/100)]n P = ₹ 12,000 n = 2 years R = 6% compounded annually Compound Interest to be paid for 2 years at the rate of 6% per annum A = P[1 + (r/100)]n A = 12000[1 + (6/100)]2 A = 12000[(100/100) + (6/100)]2 A = 12000 × (106/100) × (106/100) A = 12000 × (11236/10000) A = 12000 × 1.1236 A = 13483.20 Compound Interest = A - P = 13483.20 - 12000 = ₹ 1483.20 Compound Interest - Simple Interest = 1483.20 - 1440 = ₹ 43.20 ☛ Check: NCERT Solutions for Class 8 Maths Chapter 8 Video Solution: NCERT Solutions Class 8 Maths Chapter 8 Exercise 8.3 Question 4 Summary: I borrowed ₹ 12,000 from Jamshed at 6% per annum simple interest for 2 years. Had I borrowed this sum at 6% per annum compound interest, the extra amount I would have to pay ₹ 43.20. ☛ Related Questions: Math worksheets and
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Given: The sum = Rs 12,000 Time = \(1 \frac{1}{2}\) years Rate = 10% p.a. Formula used: A = P(1 + R/100)t Here, A, P, R and t are the Amount, Principal, Rate and time respectively Concept used: When compounded half-yearly then, Rate is half and time is doubled Calculation: Rate = 10%/2 = 5% and Time = \(1 \frac{1}{2}\) × 2 = 3 half yearly Now, A = P(1 + R/100)t ⇒ A = 12000(1 + 5/100)3 ⇒ A = 12000 × 21/20 × 21/20 × 21/20 ⇒ A = 13891.5 ∴ The total amounts to be paid is Rs 13891.50 India’s #1 Learning Platform Start Complete Exam Preparation
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Last updated at Nov. 12, 2018 by Teachoo
Example 12 What amount is to be repaid on a loan of Rs 12000 for 1 1/2 years at 10% per annum compounded half yearly. Given Principal = Rs 12000 Here, rate is compounded half yearly. Rate of interest = R = 10/2 % = 5 % & Time = 1 1/2 years = 3/2 years = 3/2 × 2 half years = 3 Amount = P (1+𝑅/100)^𝑛 = 12000 (1+5/100)^3 = 12000 (1+1/20)^3 = 12000 ((20 + 1)/20)^3 = 12000 (21/20)^3 = 12000 × 21/20 × 21/20 × 21/20 = 12 × 21/2 × 21/2 × 21/2 = 3 × 21 × 21 × 21/2 = (63 × 441)/2 = 27783/2 = 13891.5 ∴ Amount = Rs 13,891.50 Text Solution Solution : Here, interest is compounded half-yearly.So, <br> Time, `t = 3` half years<br> `:.`Rate of interest `r = 10/2 = 5% ` per half yearly<br> Loan amount, `P = "Rs." 12000` <br> So, Amount to be repaid, `A = 12000(1+5/100)^3`<br> `A = 12000xx(21/20)xx(21/20)xx(21/20) = "Rs."13891.5` |
What amount to be repaid on a loan of ₹ 12000 for 1½ years at 10% per annum compounded half yearly
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